Asynchronous sparse-MFPCA validation¶

This page records the known-truth qualification boundary for the 1.1 development-line asynchronous sparse planar MFPCA / joint-PACE path.

The target is not generic multivariate FDA optimality. The validation asks whether the implementation correctly handles coordinate-specific native observation grids, recovers the declared joint population structure in predeclared finite-sample designs, reduces to the existing synchronous estimator when observations are fully paired, and fails explicitly when cross-channel support is unavailable.

Reproducible workflow¶

The qualification is generated by:

scripts/run_sparse_mfpca_async_validation.py
.github/workflows/sparse-mfpca-async-validation.yml

The first successful scientific qualification ran on exact implementation head 86483291ce9722d9c4afde2bd399b28cdee6b9aa:

• workflow run: 37301893231;
• artifact: 11341529772;
• artifact digest: sha256:07c6d5d96f2bf46c990fb3f1259238272e35e65eb793dc7d8386e5f7614b7db6.

Later documentation-only commits are required to rerun the same deterministic gate before merge; the PR evidence record should be used for the final exact-head workflow identity.

Observation designs¶

Three deterministic known-truth designs were predeclared.

Fully paired¶

x and y share every retained native timestamp. This case tests whether the new asynchronous implementation reduces to the already-qualified synchronous fit_sparse_mfpca() path rather than defining a second incompatible estimator.

Staggered¶

x and y use independently generated sparse native grids and share only the fixed endpoints. This is the strongest direct test of the new estimand because most x and y observations are coordinate-specific.

Mixed¶

Each curve contains shared timestamps plus x-only and y-only timestamps. This exercises both the latent same-time-exclusion rule and simultaneous measurement-error cross-covariance placement within the same score system.

All designs use known analytic vector eigenfunctions, known eigenvalues, known latent scores, and declared measurement-error covariance. The estimator receives the true error covariance; the qualification does not test automatic measurement-error estimation.

Paired reduction¶

The asynchronous and synchronous estimators were fitted to the same fully paired data using the same grid, bandwidths, PSD policy, and measurement-error covariance.

Maximum absolute differences were exactly:

The paired-reduction tolerance was 1e-8. This is strong evidence that the asynchronous path is an additive generalization rather than a behavior change to the synchronous scientific contract.

Known-truth recovery¶

These values are qualification observations for these declared designs; they are not universal finite-sample guarantees.

The staggered design contained 586 x-only and 603 y-only observations across 64 curves, while retaining only 128 simultaneous x/y observations. Despite that strongly coordinate-specific layout, no score system failed and the minimum joint-subspace principal cosine remained about 0.992.

The mixed design contained 352 x-only and 360 y-only observations across 60 curves, plus 359 simultaneous observations. Its covariance and score recovery was stronger than the staggered design under the declared simulation.

Same-time latent versus error-covariance accounting¶

The implementation uses different rules for latent cross-covariance fitting and score-system measurement error:

• simultaneous x-y residual products are excluded from latent Cxy smoothing;
• declared off-diagonal measurement-error covariance is added only between simultaneous x/y scalar observations during scoring.

The qualification checked these counts exactly.

This exact equality is part of the qualification contract, not merely descriptive output.

Hidden-synchronization audit¶

Every qualified scenario retained:

raw_sparse_trajectory_interpolation_performed = false
nearest_neighbour_synchronization_performed = false
time_binning_performed = false
rank_k_covariance_used_for_scoring = false

The common evaluation grid belongs only to fitted population functions. It is not a manufactured raw observation grid.

Deterministic replay¶

The staggered design was refitted from the same retained observations and settings. Eigenvalues, eigenfunctions, scores, and fitted Cxy were exactly identical under deterministic replay.

Expected failure¶

A deliberately pathological fit used a same-time tolerance wide enough to remove all candidate asynchronous x-y residual products. The estimator failed explicitly with:

insufficient_async_cross_covariance_pairs

It did not silently synchronize coordinates, mirror marginal covariance, substitute independent x/y FPCA, or return an unqualified cross-channel estimate.

What this qualification supports¶

The evidence supports the narrow claim that the implemented 1.1 asynchronous path:

• accepts coordinate-specific native x/y observation grids through the declared union-timestamp representation;
• estimates directional asynchronous cross-covariance without hidden raw alignment;
• reuses the qualified full joint covariance/PSD/eigendecomposition machinery;
• applies correlated measurement error only to simultaneous scalar coordinate observations;
• uses the full fitted covariance in asynchronous joint-PACE scoring;
• reduces exactly to the synchronous estimator when all observations are paired;
• retains deterministic diagnostics and explicit support failures.

What this qualification does not support¶

It does not establish:

• universal recovery rates for arbitrary sparsity, noise, or missingness mechanisms;
• robustness to informative observation times beyond the package's separate diagnostics/sensitivity work;
• automatic bandwidth optimality;
• asynchronous conditional score-uncertainty calibration;
• population-estimation uncertainty propagation;
• asynchronous multilevel MFPCA;
• time-varying/heteroskedastic measurement-error models;
• device synchronization correctness;
• partial/future trajectory prediction.

Those require separate estimands and qualification programmes.